A conventional power supply for a mobile (portable) telephone set in a car is connected through an ignition (key) switch to a battery, so that an electric power is supplied to the telephone set, when the ignition switch is turned on. Therefore, when the ignition switch is turned off, the supply of an electric power is shut off to avoid unintentional consumption thereof. This structure is adopted, for the reason that electric power is consumed in the telephone set during not only an occupied state for communication, but also a waiting state for receiving a call. Consequently, the exhaustiveness of the battery is avoided by turning the ignition switch off.
However, the conventional power supply of a mobile telephone set in a car has a disadvantage in that an absentee receiving of facsimile information, an absentee (caretaking) recording of telephone message, etc. are not carried out, when an ignition key is pulled out and a driver leaves the car, so that the ignition switch is turned off to shut off the supply of an electric power to the telephone set.